An Economic Load Dispatch (ELD) algorithm seeks to allocate power output among several generating units to match customer load demand at the minimum cost. The ELD is a fundamental optimization issue to improve the operating efficiency of a power plant, especially when the load demand curve of a generating company is determined by the net sum of a set of transactions. When the dispatch problem concerns a single time interval, it is referred to as a static economic load dispatch (SELD). When the dispatch problem concerns a finite number of dispatch intervals coupled with load forecasting to provide an optimal generation trajectory tracking a varying load demand, it is referred to as a dynamic economic load dispatch (DELD) problem. Comparing the two, DELD affords a more economic solution over all generators and all time intervals. However, DELD has long been recognized as a difficult dynamic programming problem due to the dynamic nature of a power system and the large variations in customer load demand. The dynamic problem is normally solved by dividing the entire dispatch period into a number of small time intervals, over which the load is considered constant and the system is considered to be in a temporal steady state. To achieve the overall cost reduction in operating a power system, the individual static intervals should be dispatched economically subject to the static constraints at that time and the additional limits put on by a series of time dependent dynamic constraints. Due to these constraints, the search space for optimization is narrow and uneven, and therefore challenges any algorithm that tries to find the optimal dispatch solution quickly and accurately.
Although several methods such as neural networks and evolutionary programming have been used to solve the SELD problem, only quadratic programming and evolutionary computing approaches have been used to solve the DELD problem. Except for the evolutionary methods, all these numerical methods make the assumption that the fuel cost function of every unit is monotonically increasing and can be expressed either by a piecewise linear equation or a quadratic equation. Unfortunately, this is not the case in real world practical systems due to non-linear characteristics including a non-smooth and non-convex fuel cost function, ramp rate limits, and discontinuous prohibited operating zones.
Even evolutionary methods have problems when solving a DELD problem. For example, in order to satisfy the many static and dynamic constraints, evolutionary methods assign a very low fitness, and therefore a very low survival chance, to the individual corresponding to a constraint violating solution, or directly rule that individual out of the population. This kind of penalty heavily restricts the sharing of information between individuals and generations. Consequently, a high percentage of individuals will be eliminated before they can contribute to the evolution. This makes the algorithm inefficient.